Some results on parameter estimation in extended growth curve models
Identifieur interne : 001237 ( Istex/Corpus ); précédent : 001236; suivant : 001238Some results on parameter estimation in extended growth curve models
Auteurs : Qi-Guang WuSource :
- Journal of Statistical Planning and Inference [ 0378-3758 ] ; 2000.
Abstract
In this paper, estimation of parameters in extended growth curve models with arbitrary covariance matrix or uniform covariance structure or serial covariance structure is studied. Admissibility and minimaxity of the least-squares estimator of regression coefficients under matrix loss are derived. The necessary and sufficient existence conditions are obtained for the uniformly minimum risk equivariant (UMRE) estimator of regression coefficients under an affine group and a transitive group of transformations with quadratic loss and matrix loss, respectively. It is proved that no UMRE estimators of the covariance matrix V and the trace of V exist. The maximum likelihood estimator of parameters under some conditions is also discussed.
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DOI: 10.1016/S0378-3758(00)00084-7
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Admissibility and minimaxity of the least-squares estimator of regression coefficients under matrix loss are derived. The necessary and sufficient existence conditions are obtained for the uniformly minimum risk equivariant (UMRE) estimator of regression coefficients under an affine group and a transitive group of transformations with quadratic loss and matrix loss, respectively. It is proved that no UMRE estimators of the covariance matrix V and the trace of V exist. 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Admissibility and minimaxity of the least-squares estimator of regression coefficients under matrix loss are derived. The necessary and sufficient existence conditions are obtained for the uniformly minimum risk equivariant (UMRE) estimator of regression coefficients under an affine group and a transitive group of transformations with quadratic loss and matrix loss, respectively. It is proved that no UMRE estimators of the covariance matrix V and the trace of V exist. The maximum likelihood estimator of parameters under some conditions is also discussed.</abstract><qualityIndicators><score>6.272</score><pdfVersion>1.2</pdfVersion><pdfPageSize>408 x 660 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>8</keywordCount><abstractCharCount>740</abstractCharCount><pdfWordCount>6071</pdfWordCount><pdfCharCount>24047</pdfCharCount><pdfPageCount>16</pdfPageCount><abstractWordCount>106</abstractWordCount></qualityIndicators><title>Some results on parameter estimation in extended growth curve models</title><pii><json:string>S0378-3758(00)00084-7</json:string></pii><refBibs><json:item><host><author></author></host></json:item><json:item><author><json:item><name>S. Geisser</name></json:item></author><host><volume>68</volume><pages><last>250</last><first>243</first></pages><author></author><title>Biometrika</title></host><title>Sample reuse procedures for prediction of the unobserved portion of a partially observed vector</title></json:item><json:item><author><json:item><name>J.C. Lee</name></json:item></author><host><volume>83</volume><pages><last>440</last><first>432</first></pages><author></author><title>J. Amer. Statist. Assoc.</title></host><title>Prediction and estimation of growth curves with special covariance structure</title></json:item><json:item><author><json:item><name>J.C. Lee</name></json:item><json:item><name>S. Geisser</name></json:item></author><host><volume>37</volume><pages><last>256</last><first>239</first></pages><author></author><title>Sankhya Ser. A</title></host><title>Application of growth curve prediction</title></json:item><json:item><host><author></author><title>Theory of Point Estimation</title></host></json:item><json:item><author><json:item><name>R.F. Potthoff</name></json:item><json:item><name>S.N. Roy</name></json:item></author><host><volume>51</volume><pages><last>326</last><first>313</first></pages><author></author><title>Biometrika</title></host><title>A generalized multivariate analysis of variance model useful especially for growth curve problems</title></json:item><json:item><author><json:item><name>A.P. Verbyla</name></json:item><json:item><name>W.N. Venables</name></json:item></author><host><volume>75</volume><pages><last>138</last><first>129</first></pages><author></author><title>Biometrika</title></host><title>An extension of the growth curve model</title></json:item><json:item><host><author></author></host></json:item><json:item><author><json:item><name>D. Von Rosen</name></json:item></author><host><volume>31</volume><pages><last>200</last><first>187</first></pages><author></author><title>J. Multivariate Anal.</title></host><title>Maximum likelihood estimators in multivariate linear normal model</title></json:item><json:item><author><json:item><name>D. Von Rosen</name></json:item></author><host><volume>36</volume><pages><last>276</last><first>269</first></pages><author></author><title>J. Statist. Plann. Inference</title></host><title>Uniqueness conditions for maximum likelihood estimators in a multivariate linear model</title></json:item><json:item><author><json:item><name>Q.G. Wu</name></json:item></author><host><volume>69</volume><pages><last>114</last><first>101</first></pages><author></author><title>J. Statist. Plann. 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Admissibility and minimaxity of the least-squares estimator of regression coefficients under matrix loss are derived. The necessary and sufficient existence conditions are obtained for the uniformly minimum risk equivariant (UMRE) estimator of regression coefficients under an affine group and a transitive group of transformations with quadratic loss and matrix loss, respectively. It is proved that no UMRE estimators of the covariance matrix V and the trace of V exist. 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Admissibility and minimaxity of the least-squares estimator of regression coefficients under matrix loss are derived. The necessary and sufficient existence conditions are obtained for the uniformly minimum risk equivariant (UMRE) estimator of regression coefficients under an affine group and a transitive group of transformations with quadratic loss and matrix loss, respectively. It is proved that no UMRE estimators of the covariance matrix <ce:italic>V</ce:italic> and the trace of <ce:italic>V</ce:italic> exist. The maximum likelihood estimator of parameters under some conditions is also discussed.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="msc"><ce:section-title>MSC</ce:section-title><ce:keyword><ce:text>primary 62H12</ce:text></ce:keyword><ce:keyword><ce:text>secondary 62F11</ce:text></ce:keyword></ce:keywords><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Uniformly minimum risk equivariant estimator</ce:text></ce:keyword><ce:keyword><ce:text>Admissible estimator</ce:text></ce:keyword><ce:keyword><ce:text>Minimax estimator</ce:text></ce:keyword><ce:keyword><ce:text>Maximum likelihood estimator</ce:text></ce:keyword><ce:keyword><ce:text>Quadratic loss</ce:text></ce:keyword><ce:keyword><ce:text>Matrix loss</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Some results on parameter estimation in extended growth curve models</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Some results on parameter estimation in extended growth curve models</title></titleInfo><name type="personal"><namePart type="given">Qi-Guang</namePart><namePart type="family">Wu</namePart><affiliation>Institute of Systems Science, Academia Sinica, Beijing 100080, People's Republic of China</affiliation><affiliation>E-mail: gyli@issol.iss.ac.cn</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">2000</dateIssued><copyrightDate encoding="w3cdtf">2000</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">In this paper, estimation of parameters in extended growth curve models with arbitrary covariance matrix or uniform covariance structure or serial covariance structure is studied. Admissibility and minimaxity of the least-squares estimator of regression coefficients under matrix loss are derived. The necessary and sufficient existence conditions are obtained for the uniformly minimum risk equivariant (UMRE) estimator of regression coefficients under an affine group and a transitive group of transformations with quadratic loss and matrix loss, respectively. It is proved that no UMRE estimators of the covariance matrix V and the trace of V exist. The maximum likelihood estimator of parameters under some conditions is also discussed.</abstract><subject><genre>MSC</genre><topic>primary 62H12</topic><topic>secondary 62F11</topic></subject><subject><genre>Keywords</genre><topic>Uniformly minimum risk equivariant estimator</topic><topic>Admissible estimator</topic><topic>Minimax estimator</topic><topic>Maximum likelihood estimator</topic><topic>Quadratic loss</topic><topic>Matrix loss</topic></subject><relatedItem type="host"><titleInfo><title>Journal of Statistical Planning and Inference</title></titleInfo><titleInfo type="abbreviated"><title>JSPI</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">20000801</dateIssued></originInfo><identifier type="ISSN">0378-3758</identifier><identifier type="PII">S0378-3758(00)X0090-0</identifier><part><date>20000801</date><detail type="volume"><number>88</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="issue pages"><start>171</start><end>356</end></extent><extent unit="pages"><start>285</start><end>300</end></extent></part></relatedItem><identifier type="istex">399D5C41AC9703395B94348ECE84C690B1252046</identifier><identifier type="DOI">10.1016/S0378-3758(00)00084-7</identifier><identifier type="PII">S0378-3758(00)00084-7</identifier><accessCondition type="use and reproduction" contentType="copyright">©2000 Elsevier Science B.V.</accessCondition><recordInfo><recordContentSource>ELSEVIER</recordContentSource><recordOrigin>Elsevier Science B.V., ©2000</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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